Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 9x - 1$ and $ BC = 2x + 62$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {9x - 1} = {2x + 62}$ Solve for $x$ $ 7x = 63$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 9({9}) - 1$ $ BC = 2({9}) + 62$ $ AB = 81 - 1$ $ BC = 18 + 62$ $ AB = 80$ $ BC = 80$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {80} + {80}$ $ AC = 160$